What if there had been a Chaos/Fractals bubble?

 

Why does one research culture drive a bubble while another does not? COURTESY: Soap Bubbles and Chaos, Journal of Pneumatic Adventures Medium.

 

Modern Artificial Intelligence (AI) research is currently at the heart of a massive financial bubble. It might pop soon, and it might not. "AI" is seemingly everywhere, although its actual value is yet to be determined. I remember learning how to program GPUs in the period around 2010 for applications to computational biology, never thinking that an esoteric research topic could become elemental in propping up the tech economy.

This got me to thinking about what it would look like if we switched out one research area for another, just to highlight any potential absurdities of the situation. So imagine if the field of Chaos and Fractals, quite popular to the point of cliche in the 1980s, was the subject of a financial bubble. It is of note that chaos and fractals were definitely hyped in their time, being featured in movies such as Star Trek: the Wrath of Khan (the Genesis Effect scene) and Ian Malcolm's rhetoric in Jurassic Park. Interestingly, advances in chaos and fractals in particular relied on advances in computing power, initially with supercomputing, and later with GPUs, parallel computing, and quantum computing [1].

In the formative years of chaos, people such as the Eds (Ott and Lorenz) [2, 3] produced a paradigm shift in how complex systems were viewed. The visualization of chaos in the form of fractals were advanced by Benoit Mandelbrot [4]. Fractals were likewise a paradigm shift in how complex phenomena were visualized. In particular, fractals visualize various aspects of chaos using non-Euclidean geometries and relatively simple sets of equations. Their popularity was advanced by a convenient shorthand: visualizations that captured the imagination. While slogans and pretty pictures captured the imagination, the popular imagination got quite far ahead of methodological rigor. This is reminiscent of claims that ascribe properties like sentience or superintelligence to AI systems.

Is this science, or inspiration, or both? Please don't financialize this. COURTESY: Moss and Fog blog.

Eventually, enthusiasm for chaos and fractals regressed back into the fields of physics and mathematics, while also becoming specialized tools for fields like finance. In short, the field matured without the irrational influx of cash, roughly following a Gartner hype cycle. This is curious in light of the limits of AI that people discuss today: regardless of whether or not AI exhibits "true" intelligence, AI systems require intense computational resources to merely be evocative of biological intelligence. But what if there is not a missing component of the intelligence simulation, but of the way in which the underlying system is modeled? Chaos and fractals are not the product of reductionist relationships (as science had been done before), but rather the product of system dynamics, recursivity, and a sensitivity to initial condition. This was the main insight of chaos and fractals, but apparently those insights are not worth a large-scale financial bubble [5].

In their time, fractals were derided as "pretty pictures", and eventually, the pretty pictures could not keep up with methodological trends across the different sciences. But fractals did provide at least one serious insight: systems that look regular at one scale exhibit irregularities apparent at other scales. This has been popularized by the Powers of 10 idea, and further applied to ideas like the coastline paradox. What is particularly interesting to a person who likes complexity approaches to science is that standard hypothesis testing was exposed to many of the same criticisms as chose and fractals. This is despite much more serious consequences of the unaddressed issues with NHST, and has persisted as the scientific norm in spite of superior methods. Quite an interesting exercise in methodological inertia. 

In the current era, AI has partially been driven by advances in methodology, but also by advances in hardware. Central to this has been NVIDIA and their GPU architecture. While GPUs have done much of the heavy lifting in the current AI summer, it is important to remember the origins of GPUs: as a graphical processing tool. This parallels how advances in computing and computational power suddenly opened up our ability to solve and plot the equations of fractal growth and other structures. Perhaps the experience of chaos and fractals will guide AI research after the bubble bursts.

References:

[1] Kaboudian, A., Cherry, E.M., and Fenton, F.H. (2019). Large-scale interactive numerical experiments of chaos, solitons and fractals in real time via GPU in a web browser. Chaos, Solitons & Fractals, 121, 6-29.

[2] Motter, A. and Campbell, D.K. (2013). Chaos at Fifty. Physics Today, 66(5).

[3] Viswanath, D. (2004). The fractal property of the Lorenz attractor. Physica D, 190, 115–128.

[4] Mandelbrot, B.B. and Blumen, A. (1989). Fractal Geometry: What is it, and What Does it do? Royal Society A, 423(1864), 3–16.

[5] Notice that I said "large-scale", which is the distinction between overeager commercialization and financialization. Perhaps financialization is a feature of 21st century popularity, but there does seem to be a difference that makes its way into scientific practice. Fractals are used extensively in attempts to understand the stochastic nature of markets, and have been commercialized in line with that expectation. 

The connections between fractals, efficient markets, and to a lesser extent chaotic behavior is exemplified in books such as:  Peters, E. (1994). Fractal Market Analysis. Wiley.

Saturday Morning NeuroSim Discussion Thread: Causality

Over the past three years, the Saturday Morning NeuroSim group has met weekly on Saturdays (mornings in North America). The Saturday Morning format continues in the tradition of Saturday Morning Physics and covers a wide variety of topics.

Our discussion thread on causality begins with Causality and Circles on May 13. From a Mastodon post by Yohan John, we considered how spatialized diagrams are confused with temporal sequences in a feedback loop. We also covered three papers in this session.

Vernon, D., Lowe, R., Thill, S., and Ziemke, T. (2015). Embodied cognition and circular causality: on the role of constitutive autonomy in the reciprocal coupling of perception and action. Frontiers in Psychology, 6, 1660.

Raginsky, M. (2023). Directed Information and Pearl’s Causal Calculus. arXiv, 1110.0718.

Laland, K.N., John Odling-Smee, J., Hoppitt, W., and Uller, T. (2013). More on how and why: cause and effect in biology revisited. Biological Philosophy, 28, 719–745.

Our conversation continued after the last week of Neuromatch Academy, when the NMA curriculum featured causal networks. Our July 29 meeting featured a collection of references on Bayesianism, Probabilistic Graphical Models, methods of integration, time-series applications, and more. Some core readings are given below.

Stanford Encyclopedia of Philosophy: causal models. This article takes an epistemological approach and provides us with a baseline for structural equation model, graphical probabilistic models, and other statistical formulations of causal relationships.

Daphne Koller’s Probabilistic Graphical Models course. Hosted on Stanford University’s Open Classroom platform, this course includes units on representation, inference, learning, and causation. The causation unit covers decision theory, utility functions, influence diagrams, and the notion of perfect information.

Pearl, J. (2000). Causality. Cambridge Press, Cambridge, UK. This classic book by Judea Pearl builds from a theory of inferred causation, starting at causal diagrams, and continuing through direct effects, indirect effects, confounds, counterfactuals, bounding effects, and probabilities. The book also covers structural models, decision analysis, and Simpson’s Paradox as the basis for methods for detecting causal relationships.

Scholkopf, B. (2019). Causality for Machine Learning. arXiv, 1911.10500.

Heckman, J.J. (2005). The Scientific Model of Causality. Sociological Methodology, 35, 1–97. Causality from an econometrics point-of-view. Counterfactuals are a set of possible outcomes generated by determinants. A causal effect is defined by the change in the manipulated factor where amongst a set of factors, in a situation where all but one is held constant.

Taskesen, E. (2021). A step-by-step guide in detecting causal relationships using Bayesian structure learning in Python. Towards Data Science, September 7.

Which variables have a direct causal effect on a target variable? Hint: association and correlation are not equivalent to causation.

Bayesian Models:

Neuberg, L.G. (2003). Causality: models, reasoning, and inference. Econometric Theory, 19, 675–685.

Pearl, J. (2001). Bayesianism and causality, or, why I am only a half-Bayesian. In “Foundations of Bayesianism”, pgs. 19–36. Kluwer Press.

Methods of Interaction: networks and non-directional graphs, as opposed to directed acyclic graphs (DAGs), require a different set of considerations. The methods below cover highly interacting systems like graphs and how change over time can be properly interpreted as causal.

Leng, S., Ma, H., Kurths, J., Lai, Y-C., Lin, W., Aihara, K., and Chen, L. (2020). Partial cross mapping eliminates indirect causal influences. Nature Communications, 11, 2632.

Park, S.H., Ha, S., and Kim, J.K. (2023). A general model-based causal inference method overcomes the curse of synchrony and indirect effects. Nature Communications, 14, 4287.

From the Granger Causality Wikipedia entry.

Time-series using Granger Causality: the first two references apply Granger Causality to time-series datasets. In such cases, the datapoints are dependent with respect to time. Given two time-series x and y, x is the cause of y if x predicts y (lagged with respect to x over a certain time interval) given x and prior values of y. This is in comparison with simply predicting the current value of y given previous values of y, which would be the counterfactual case.

The final paper in the group (Stokes and Purdon) critiques Granger Causality from a Neuroscience perspective.

Carlos‐Sandberg, L. and Clack, C.D. (2021). Incorporation of causality structures to complex network analysis of time‐varying behaviour of multivariate time series. Scientifc Reports, 11, 18880.

Runge, J., Nowack, P., Kretschmer, M., Flaxman, S., Sejdinovic, D. (2019). Detecting and quantifying causal associations in large nonlinear time series datasets. Science Advances, 5(11), aau4996.

Stokes, P.A. and Purdon, P.L. (2017). A study of problems encountered in Granger causality analysis from a neuroscience perspective. PNAS, 114(34), E7063-E7072.

The third session (August 5) was a focus on causality specifically as it is treated in Neuroscience. This session followed up on a Twitter debate by Kording Lab and Earl Miller about the role of causality in neuroscience. The consensus to the question “Why is Neuroscience so into causality?” was that it provides a means to identify mechanisms for function. Causality in neuroscience differs from philosophical discussions about causality in that Neuroscience must infer causality from data, while philosophers (and statisticians) do the work of proving causality.

One interesting point from Kording Lab is that there is a difference between proximate causes and ultimate causes. In some fields, causality is obvious and so causal methods are not always necessary. But Neuroscience is partially about the behavioral substrate, and so we can turn to Niko Tinbergen’s four questions. The four questions concern 1) how a trait arose in development (proximate, dynamic), 2) how a trait arose in evolution (ultimate, dynamic), 3) what is the mechanism or structure of a trait (proximate, static), and 4) what is the adaptive value or function of a trait (ultimate, static).

You can read more about Tinbergen’s four questions and their causal implications in the following papers.

Beer, C. (2020). Niko Tinbergen and questions of instinct. Animal Behaviour, 164, 261–265.

Nesse, R.M. (2019). Tinbergen’s four questions: two proximate, two evolutionary. Evolution, Medicine, and Public Health, 2, doi:10.1093/ emph/eoy035.

Mayr, E. (1961). Cause and effect in biology. Science, 134, 1501–1506.

The other papers from this session focused on mental representations and causal functional connectivity in the brain, respectively.

Sloman, S.A. and Lagnado, D. (2015). Causality in Thought. Annual Reviews in Psychology, 66, 223–247.

While Bayesian approaches are good for theory-building, they are an incomplete account of what goes on in the cognitive world.

Biswas, R. and Shlizerman, E. (2022). Statistical perspective on functional and causal neural connectomics: The Time-Aware PC algorithm. PLoS Computational Biology, 18(11), e1010653.

The fourth session (August 19) picks up on a point covered in the second session, namely how causality can be inferred from network data. This covers related ideas of transitivity, weak interactions, and anti-causal models. Papers for this session include networks in ecology, anticipative and non-anticipative control theory, and anti-causal systems.

Typology of causal models for past, present, and future events.

Naghshtabrizi, P. and Hespanha, J.P. (2006). Anticipative and non-anticipative controller design for network control systems. Lecture Notes in Control and Information Science, 331.

Sugihara, G., May, R., Ye, H., Hsieh, C-H., Deyle, E., Fogarty, M., Munch, S. (2012). Detecting Causality in Complex Ecosystems. Science, 338, 496–500.

Chattopadhyay, I. (2014). Causality Networks. arXiv, 1406.6651.

Anticausal System. Wikipedia.

McCurdy, T. (2007). Causal Systems: understanding the basics. Physics Forums. September 23.

From the Necessity and Sufficiency Wikipedia entry.

Finally, some fields (cell and molecular biology) have working models of causation that while useful, are not particularly illuminating. In the cell and molecular biology example, the traditional model of necessity and sufficiency (a mechanism being necessary but not sufficient) can be criticized for not being complete with respect to incorporating counterfactuals or multiple potential causes. See this paper for more information:

Bizzarri, M., Brash, D.E., Briscoe, J., Grieneisen, V.A., Stern, C.D., and Levin, M. (2019). A call for a better understanding of causation in cell biology. Nature Reviews Molecular Cell Biology, 20, 261–262.

New Paper on Developmental Braitenberg Vehicles now live!

 

The special issue of Artificial Life on Embodied Intelligence is now live! Inside you will find our paper "Braitenberg Vehicles as Developmental Neurosimulation", which has lived on the arXiv since 2020. This paper lays out an approach to Developmental Neurosimulation, involving three adversarial approaches to the agent-based development of embodied brains and embodied cognition. Here is the abstract:

Connecting brain and behavior is a longstanding issue in the areas of behavioral science, artificial intelligence, and neurobiology. As is standard among models of artificial and biological neural networks, an analogue of the fully mature brain is presented as a blank slate. However, this does not consider the realities of biological development and developmental learning. Our purpose is to model the development of an artificial organism that exhibits complex behaviors. We introduce three alternate approaches to demonstrate how developmental embodied agents can be implemented. The resulting developmental Braitenberg vehicles (dBVs) will generate behaviors ranging from stimulus responses to group behavior that resembles collective motion. We will situate this work in the domain of artificial brain networks along with broader themes such as embodied cognition, feedback, and emergence. Our perspective is exemplified by three software instantiations that demonstrate how a BV-genetic algorithm hybrid model, a multisensory Hebbian learning model, and multi-agent approaches can be used to approach BV development. We introduce use cases such as optimized spatial cognition (vehicle-genetic algorithm hybrid model), hinges connecting behavioral and neural models (multisensory Hebbian learning model), and cumulative classification (multi-agent approaches). In conclusion, we consider future applications of the developmental neurosimulation approach.

There are many themes to follow up on in this paper. Just of few examples include:

* brain/body scaling in an embodied agent.

* the role of multisensory integration in the development of cognition.

* ways to classify shapes and motifs in the emergence of multi-agent collectives. 

* spatial cognition and transfer learning in developmental embodied systems.

Congratulations to Stefan Dvoretskii, Ziyi Gong, Ankit Gupta, Jesse Parent, and Bradly Alicea for their hard work.

Google Summer of Code 2022 in the OpenWorm Community (DevoWorm)

Welcome to Google Summer of Code 2022! I am pleased to announce that this year, we have two funded projects: D-GNNs and Digital Microspheres! These projects will both take place in conjunction with the DevoWorm part of the OpenWorm community. DevoWorm is an interdisciplinary group engaged in both computational and biological data analysis. We have weekly meetings on Jit.si, and are a part of the OpenWorm Foundation. 

This year, we were able to fund two students per project. They will be working on complementary solutions to each problem, and we will see how far they get by the end of the Summer. 

D-GNNs (Developmental Graph Neural Networks)

The description for this project is as follows:

Biological development features many different types of networks: neural connectomes, gene regulatory networks, interactome networks, and anatomical networks. Using cell tracking and high-resolution microscopy, we can reconstruct the origins of these networks in the early embryo. Building on our group's past work in deep learning and pre-trained models, we look to apply graph neural networks (GNNs) to developmental biological analysis.

The contributor will create graph embeddings that resemble actual biological networks found throughout development. Potential activities include growing graph embeddings using biological rules, differentiation of nodes in the network, and GNNs that generate different types of movement output based on movement seen in microscopy movies. The goal is to create a library of GNNs that can simulate developmental processes by analyzing time-series microscopy data.

When completed, D-GNNs will become part of the DevoWorm AI library. Ultimately, we will be integrating the GNN work with the DevoLearn (open-source pre-trained deep learning) software. 

Jiahang Li

Jiahang Li is a first year MPhil candidate in Computing Department at Hong Kong Polytechnic University. His research interests cover graph representation learning and its applications. Jiahang's approach to the project is to provide a pipeline that converts microscopic video data of C. elegans and other organisms into graph structures, on which advanced network analysis techniques and graph neural networks will be employed to obtain high-level representation of embryogenesis and to solve applied problems.

Wataru Kawakami

Wataru is a student at Kyoto University with interests in Machine Learning (in particular Graph Neural Networks) and Neuroimaging.

Digital Microspheres

The description for this problem is as follows: 

This project will build upon the specialized microscopy techniques to develop a shell composed of projected microscopy images, arranged to represent the full external surface of a sphere. This will allow us to create an atlas of the embryo’s outer surface, which in some species (e.g. Axolotl) enables us to have a novel perspective on neural development.

The contributor will build a computational tool that allows us to visualize 4D data derived from the surface of an Axolotl embryo. The spatial model and animation (4th dimension) of microscopy image data can be created in a 3-D modeling software of your choice.

This project is based on previous research by DevoWorm contributors Richard Gordon and Susan Crawford-Young. The flipping and ball microscopy research involve the design and fabrication of specialized microscopes to image embryos in a 4-D context (3 dimensions of space plus time).

Spherical Embryo Maps: Gordon, R. (2009). Google Embryo for Building Quantitative Understanding of an Embryo As It Builds Itself. II. Progress Toward an Embryo Surface Microscope. Biological Theory, 4, 396–412.

Flipping Microscopy: Crawford-Young, S., Dittapongpitch, S., Gordon, R., and Harrington, K. (2018). Acquisition and reconstruction of 4D surfaces of axolotl embryos with the flipping stage robotic microscope. Biosystems, 173, 214-220.

Ball Microscopy: Crawford-Young, S.J. and Young Williment, J.L. (2021). A ball microscope for viewing the entire surface of amphibian embryos. Biosystems, 208, 104498.

Karan Lohaan

Karan is a student at Amrita Vishwa Vidyapeetham University, and is a member of the AMFoss program there. He is interested in Machine Learning and Image Processing. 

Harikrishna Pillai

I am Harikrishna pursuing my B.Tech in Computer Science and Artificial Intelligence from Amrita Vishwa Vidyapeetham University. I completed my schooling in Mumbai. I started with python as my first language and eventually developed interest for AI. Due to my interest in Android apps, I have done Android development in Kotlin. Also, I have been interested in open source for some time now and therefore, I wanted to start my open source journey with GSoC.

We also have two GSoC mentors for these projects: Bradly Alicea is a mentor for D-GNNs and Digital Microspheres, and Jesse Parent is a mentor for D-GNNs. Richard Gordon and Susan Crawford-Young are serving as collaborators for the Digital Microspheres project.

If you would like to check on their progress, please check out our weekly meetings available on our YouTube channel.

Dispatches from the Emergent Interaction Workshop

 This content has been cross-posted at the Orthogonal Lab Medium.

Last month, the Orthogonal Lab was represented at the Emergent Interaction Workshop (part of SIGCHI 2021). We contributed a paper titled “Allostasis Machines: a model for understanding internal states and technological environments”, with a companion presentation now on YouTube. Thanks go to Bradly Alicea, Daniela Cialfi, Anson Lim, and Jesse Parent for their contribution. We are planning an expanded version of this work with Rishabh Chakraborty that will demonstrate Allostasis Machines as a Reinforcement Learning implementation.

The subtitle of this workshop was “Complexity, Dynamics, and Enaction in HCI”. Therefore, the focus was on advancing measurement and theory, in addition to better characterize complexity in the field of Human-Computer Interaction. The four-hour long session was summarized in our weekly meeting on May 22. I have also provided supplemental readings in four workshop-related categories at the bottom of this post.

Overview of the Emergent Interaction Miro board.

There were six other papers made available before the session. Two of the most interesting to the Orthogonal Lab group are “Fields of Affordances and Human Computer Interaction” by Jelle Bruineberg and “Simulating Social Acceptability With Agent-based Modeling” by Alarith Uhde and Marc Hassenzahl.

The Emergent Interaction utilized Zoom, Slack, and a Miro board to enable discussion during the session. Check out the overview paper titled “Emergent Interaction: Complexity, Dynamics, and Enaction in HCI” for more information.

Testing, 1, 2, Emergent T-shirt….

There were a number of interesting and innovative topics discussed in the workshop. Dynamical approaches came up several times, along with topics such as multifractality, attractor analysis, and co-evolutionary experimental design. For more information regarding the first two topics, check out Alan Dix’s blog on Making Sense of Quantitative Data, and Dan Bennett’s preprint “Multifractal Mice: Measuring Task Engagement and Readiness-to-hand via Hand Movement”.

Tom Froese presented on his Enactive Artificial Intelligence and HCI work. His Google Scholar profile features some really interesting work that cuts across the worlds of Artificial Life, Cybernetics, and Cognitive Science, but his workshop topic was how modern Machine Learning approaches are insufficiently embodied. I have posted references to two of his key works (workshop-wise) in the Further Readings section of this post.

Later, Parisa Eslambolchilar presented on first-order closed-loop feedback taking the form of sensor-based human interaction loops. She reviewed some of the things she developed in her Doctoral dissertation, then lead us into her more recent work. Learn more by reading “A Model-Based Approach to Analysis and Calibration of Sensor-based Human Interaction Loops”.

Then, Vassilis Kostakos discussed his work on modeling interactions between technology users (or users and interfaces) as a complex system. He utilized the “lynx-hare” predator-prey analogy, inspired by Lotka-Volterra co-evolutionary dynamics. Read more in this paper published last year in Human-Computer Interaction: “Modeling interaction as a complex system”.

Emergent Interaction is now on Twitter! Give them a follow to join the discussion.

Further Reading: Measurement techniques.

Rebout, N., Lone, J-C., De Marco, A., Cozzolino, R., Lemasson, A., and Thierry, B. (2021). Measuring complexity in organisms and organizations. Royal Society Open Science, 8, 200895.

Zhou, Q., Chua, C-C., Knibbe, J., Goncalves, J., and Velloso, E. (2021). Dance and Choreography in HCI: A Two-Decade Retrospective. Proceedings of CHI, 262, 1–14. Video

Further Reading: Enactive Approaches to Artificial Systems.

Froese, T. and Ziemke, T. (2009). Enactive artificial intelligence: Investigating the systemic organization of life and mind. Artificial Intelligence, 173, 466–500.

Froese, T., McGann, M., Bigge, W., Spiers, A., and Seth, A.K. (2012). The Enactive Torch: A New Tool for the Science of Perception. IEEE Transactions on Haptics, 5(4), 365–375.

Further Reading: Agent-based Modeling approaches.

Bonabeau, E. (2002). Agent-based modeling: Methods and techniques for
simulating human systems. PNAS, 99(3), 7280–7287.

Grimm, V., Revilla, E., Berger, U., Jeltsch, F., Mooij, W.M., Railsback, S.F., Thulke, H-H., Weiner, J., Wiegand, T., and DeAngelis, D.L. (2005).
Pattern-Oriented Modeling of Agent-Based Complex Systems: Lessons from Ecology. Science, 310, 987.

Further Reading: Criticalities and Characterizing Systems.

Dotov, D.G., Nie, L., and Chemero, A. (2010). A Demonstration of the Transition from Ready-to-Hand to Unready-to-Hand. PLoS One, 5(3), e9433.

Kelso, J.A.S. (2021). Unifying Large-and Small-Scale Theories of Coordination. Entropy, 23(5), 537.